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A207873 Numerator of Z(n,1/2), where Z(n,x) is the n-th Zeckendorf polynomial. 5
1, 1, 1, 5, 1, 9, 5, 1, 17, 9, 5, 21, 1, 33, 17, 9, 41, 5, 37, 21, 1, 65, 33, 17, 81, 9, 73, 41, 5, 69, 37, 21, 85, 1, 129, 65, 33, 161, 17, 145, 81, 9, 137, 73, 41, 169, 5, 133, 69, 37, 165, 21, 149, 85, 1, 257, 129, 65, 321, 33, 289, 161, 17, 273, 145, 81, 337 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

The Zeckendorf polynomials Z(x,n) are defined and ordered at A207813.  See A207872 for denominators to match A207873.

LINKS

Table of n, a(n) for n=1..67.

MATHEMATICA

fb[n_] := Block[{k = Ceiling[Log[GoldenRatio, n*Sqrt[5]]], t = n, fr = {}}, While[k > 1, If[t >= Fibonacci[k], AppendTo[fr, 1]; t = t - Fibonacci[k],

    AppendTo[fr, 0]]; k--]; fr]; t = Table[fb[n],

      {n, 1, 500}];

b[n_] := Reverse[Table[x^k, {k, 0, n}]]

p[n_, x_] := t[[n]].b[-1 + Length[t[[n]]]]

Table[p[n, x], {n, 1, 40}]

Denominator[Table[p[n, x] /. x -> 1/2,

   {n, 1, 120}]]                       (* A207872 *)

Numerator[Table[p[n, x] /. x -> 1/2,

   {n, 1, 120}]]                       (* A207873 *)

CROSSREFS

Cf. A207813, A207873.

Sequence in context: A094650 A189234 A199736 * A198671 A129343 A342634

Adjacent sequences:  A207870 A207871 A207872 * A207874 A207875 A207876

KEYWORD

nonn

AUTHOR

Clark Kimberling, Feb 21 2012

STATUS

approved

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Last modified May 9 04:53 EDT 2021. Contains 343687 sequences. (Running on oeis4.)